all_task<- cbind(s2r_abs,s2v_abs) %>%
select(sid, frame_effect_r, frame_effect_v, frame_size)
p_df<- perception_abs %>%
ungroup() %>%
select(magnitude, sid) %>%
rename(sub_1 =sid)
all_task<- cbind(all_task,p_df)
all_task<- all_task %>%
select(-sub_1)
all_task<-all_task %>%
rename(vv= frame_effect_v,
oc = frame_effect_r,
perc = magnitude)
To determine the change in PSE as a function of frame size, we subtracted the PSE for counterclockwise trials from clockwise trials, and then divided that by half.
A negative value indicates that participants PSEs are being
biased in the opposite direction of the tilt of the frame.
| Frame Size | Mean | Median | SD | Min | Max |
|---|---|---|---|---|---|
| Small | 2.11 | 2.00 | 1.15 | -0.27 | 6.35 |
| Medium | 1.91 | 1.71 | 1.12 | 0.15 | 6.68 |
| Large | 1.71 | 1.45 | 1.02 | -0.06 | 4.77 |
| Extra Large | 1.55 | 1.33 | 0.99 | -0.50 | 5.80 |
Perception Task: RFI | |||||||
|---|---|---|---|---|---|---|---|
frame_size | estimate | statistic | p | parameter | Method | Alternative | 95% CI |
175 | 2.11 | 16.44 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.85, 2.37] |
410 | 1.91 | 15.27 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.66, 2.16] |
645 | 1.71 | 14.97 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.48, 1.93] |
880 | 1.55 | 14.03 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.33, 1.77] |
p_mag_anova<- aov(frame_effect_perception ~frame_size, data =perception)
summary(p_mag_anova)
## Df Sum Sq Mean Sq F value Pr(>F)
## frame_size 3 14.3 4.759 4.154 0.0066 **
## Residuals 316 362.0 1.146
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
tukey_p<-tukey_hsd(p_mag_anova)
apa_table(tukey_p)
| term | group1 | group2 | null.value | estimate | conf.low | conf.high | p.adj | p.adj.signif |
|---|---|---|---|---|---|---|---|---|
| frame_size | 175 | 410 | 0.00 | -0.20 | -0.64 | 0.24 | 0.63 | ns |
| frame_size | 175 | 645 | 0.00 | -0.40 | -0.84 | 0.03 | 0.08 | ns |
| frame_size | 175 | 880 | 0.00 | -0.56 | -1.00 | -0.12 | 0.01 | ** |
| frame_size | 410 | 645 | 0.00 | -0.20 | -0.64 | 0.24 | 0.64 | ns |
| frame_size | 410 | 880 | 0.00 | -0.36 | -0.80 | 0.08 | 0.15 | ns |
| frame_size | 645 | 880 | 0.00 | -0.16 | -0.60 | 0.28 | 0.78 | ns |
The results between the table and graph are inconsistent due to different tests being used. I am unsure whether I need to use the Tukey HSD test ( shown in the table above) or if a Bonferroni correction is more appropriate (used in the violin graph below).
The effect of the frames was quantified by subtracting the mean errors for the counterclockwise-tilted frames from those of the clockwise-tilted frames then halving this value to get a measure of the average effect of a single frame (negative values indicated eye movements that deviated in the direction opposite the tilt of the frame).
| Frame Size | Mean | Median | SD | Min | Max |
|---|---|---|---|---|---|
| Small | 1.47 | 1.31 | 1.63 | -2.77 | 8.74 |
| Medium | 1.23 | 1.01 | 1.75 | -1.84 | 8.34 |
| Large | 1.14 | 1.04 | 1.35 | -1.63 | 5.91 |
| Extra Large | 1.04 | 0.88 | 1.51 | -2.10 | 8.97 |
s2v_ttest_df<-saccade_to_vert_magnitude %>% group_by(FRAME_SIZE_VAL) %>% do(tidy(t.test(.$frame_effect_v)))
nice_table(s2v_ttest_df)
FRAME_SIZE_VAL | estimate | statistic | p | parameter | Method | Alternative | 95% CI |
|---|---|---|---|---|---|---|---|
175 | 1.47 | 8.04 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.11, 1.83] |
410 | 1.23 | 6.29 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.84, 1.62] |
645 | 1.14 | 7.55 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.84, 1.44] |
880 | 1.04 | 6.16 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.70, 1.37] |
vv_mag_anova<- aov(frame_effect_v~FRAME_SIZE_VAL, data =saccade_to_vert_magnitude)
#summary(vv_mag_anova)
tukey_vv<-tukey_hsd(vv_mag_anova)
apa_table(tukey_vv)
| term | group1 | group2 | null.value | estimate | conf.low | conf.high | p.adj | p.adj.signif |
|---|---|---|---|---|---|---|---|---|
| FRAME_SIZE_VAL | 175 | 410 | 0.00 | -0.24 | -0.88 | 0.40 | 0.77 | ns |
| FRAME_SIZE_VAL | 175 | 645 | 0.00 | -0.33 | -0.97 | 0.31 | 0.56 | ns |
| FRAME_SIZE_VAL | 175 | 880 | 0.00 | -0.43 | -1.07 | 0.21 | 0.31 | ns |
| FRAME_SIZE_VAL | 410 | 645 | 0.00 | -0.09 | -0.73 | 0.55 | 0.98 | ns |
| FRAME_SIZE_VAL | 410 | 880 | 0.00 | -0.19 | -0.83 | 0.45 | 0.87 | ns |
| FRAME_SIZE_VAL | 645 | 880 | 0.00 | -0.10 | -0.75 | 0.54 | 0.98 | ns |
## `geom_smooth()` using formula = 'y ~ x'
The effect of the frames was quantified by subtracting the mean errors for the counterclockwise-tilted frames from those of the clockwise-tilted frames then halving this value to get a measure of the average effect of a single frame (negative values indicated eye movements that deviated in the direction opposite the tilt of the frame).
| Frame Size | Mean | Median | SD | Min | Max |
|---|---|---|---|---|---|
| Small | -1.61 | -1.50 | 1.44 | -6.47 | 4.51 |
| Medium | -0.88 | -0.99 | 1.24 | -4.38 | 2.39 |
| Large | -0.62 | -0.58 | 1.35 | -4.01 | 4.02 |
| Extra Large | -0.76 | -0.70 | 1.14 | -4.76 | 2.57 |
FRAME_SIZE_VAL | estimate | statistic | p | parameter | Method | Alternative | 95% CI |
|---|---|---|---|---|---|---|---|
175 | -1.61 | -9.98 | < .001*** | 79.00 | One Sample t-test | two.sided | [-1.93, -1.29] |
410 | -0.88 | -6.36 | < .001*** | 79.00 | One Sample t-test | two.sided | [-1.15, -0.60] |
645 | -0.62 | -4.09 | < .001*** | 79.00 | One Sample t-test | two.sided | [-0.92, -0.32] |
880 | -0.76 | -5.94 | < .001*** | 79.00 | One Sample t-test | two.sided | [-1.01, -0.50] |
# oc_mag_anova<- aov(frame_effect_r~FRAME_SIZE_VAL, data =saccade_to_rod_magnitude)
# summary(oc_mag_anova)
# tukey_oc<-tukey_hsd(oc_mag_anova)
# apa_table(tukey_oc)
## Df Sum Sq Mean Sq F value Pr(>F)
## FRAME_SIZE_VAL 3 46.9 15.635 9.284 6.7e-06 ***
## Residuals 316 532.2 1.684
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| term | group1 | group2 | null.value | estimate | conf.low | conf.high | p.adj | p.adj.signif |
|---|---|---|---|---|---|---|---|---|
| FRAME_SIZE_VAL | Small | Medium | 0.00 | 0.73 | 0.20 | 1.26 | 0.00 | ** |
| FRAME_SIZE_VAL | Small | Large | 0.00 | 0.99 | 0.46 | 1.52 | 0.00 | **** |
| FRAME_SIZE_VAL | Small | Extra Large | 0.00 | 0.85 | 0.32 | 1.38 | 0.00 | *** |
| FRAME_SIZE_VAL | Medium | Large | 0.00 | 0.26 | -0.27 | 0.79 | 0.58 | ns |
| FRAME_SIZE_VAL | Medium | Extra Large | 0.00 | 0.12 | -0.41 | 0.65 | 0.94 | ns |
| FRAME_SIZE_VAL | Large | Extra Large | 0.00 | -0.14 | -0.67 | 0.39 | 0.90 | ns
|
So far the perceptual and orientation contrast effect were reported as negative numbers, indicating that the perceptual response or saccade erred in the opposite direction of the tilt of the frame. However, it should be noted that for the purpose of making an additive comparison between summed saccade tasks and the perceptual response, we used the inverse value of the OC effect.
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between across_frames$perception and
## across_frames$combined_saccade is positive, statistically significant, and very
## large (r = 0.43, 95% CI [0.33, 0.51], t(318) = 8.45, p < .001)
## `geom_smooth()` using formula = 'y ~ x'
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between across_frames$perception and
## across_frames$combined_saccade is positive, statistically significant, and very
## large (r = 0.43, 95% CI [0.33, 0.51], t(318) = 8.45, p < .001)
## `geom_smooth()` using formula = 'y ~ x'
Perception and Saccade-to-Vertical
## `geom_smooth()` using formula = 'y ~ x'
Perception and Saccade-to-Rod
## `geom_smooth()` using formula = 'y ~ x'
For each frame size a hierarchical design was employed using two models: 1) model 1 predicted the overall RFI magnitude (measured by the perception task) from the visuovestibular effect (measured by the saccade-to-vertical task) and 2) model 2 predicted the overall RFI magnitude from visuovestibular effect and the orientation contrast effect (measured by the saccade-to-rod task).
##
## Call:
## lm(formula = perc ~ vv, data = df_small)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4004 -0.7165 -0.1283 0.4315 4.2230
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.12753 0.17419 12.214 <2e-16 ***
## vv -0.01199 0.07954 -0.151 0.881
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.155 on 78 degrees of freedom
## Multiple R-squared: 0.0002913, Adjusted R-squared: -0.01253
## F-statistic: 0.02273 on 1 and 78 DF, p-value: 0.8805
##
## Call:
## lm(formula = perc ~ vv + oc, data = df_small)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4789 -0.6643 -0.1876 0.3187 4.2826
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.83034 0.21902 8.357 2.08e-12 ***
## vv -0.01792 0.07779 -0.230 0.8184
## oc -0.19003 0.08810 -2.157 0.0341 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.129 on 77 degrees of freedom
## Multiple R-squared: 0.05726, Adjusted R-squared: 0.03277
## F-statistic: 2.338 on 2 and 77 DF, p-value: 0.1033
## [1] 0.05696534
## Analysis of Variance Table
##
## Model 1: perc ~ vv
## Model 2: perc ~ vv + oc
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 78 104.12
## 2 77 98.19 1 5.9331 4.6527 0.03412 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | 2.128 | 1.830 |
| (0.174) | (0.219) | |
| vv | -0.012 | -0.018 |
| (0.080) | (0.078) | |
| oc | -0.190 | |
| (0.088) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.000 | 0.057 |
| R2 Adj. | -0.013 | 0.033 |
| AIC | 254.1 | 251.4 |
| BIC | 261.3 | 260.9 |
| Log.Lik. | -124.057 | -121.710 |
| RMSE | 1.14 | 1.11 |
## [1] 0.0631005
## Analysis of Variance Table
##
## Model 1: perc ~ vv
## Model 2: perc ~ vv + oc
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 78 80.926
## 2 77 74.703 1 6.2227 6.4141 0.01336 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | 1.575 | 1.391 |
| (0.140) | (0.153) | |
| vv | 0.270 | 0.258 |
| (0.065) | (0.064) | |
| oc | -0.228 | |
| (0.090) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.179 | 0.242 |
| R2 Adj. | 0.169 | 0.223 |
| AIC | 234.0 | 229.5 |
| BIC | 241.1 | 239.1 |
| Log.Lik. | -113.975 | -110.775 |
| RMSE | 1.01 | 0.97 |
## [1] 0.08649254
## Analysis of Variance Table
##
## Model 1: perc ~ vv
## Model 2: perc ~ vv + oc
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 78 69.863
## 2 77 62.747 1 7.1162 8.7326 0.004146 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | 1.373 | 1.284 |
| (0.139) | (0.136) | |
| vv | 0.293 | 0.248 |
| (0.079) | (0.076) | |
| oc | -0.227 | |
| (0.077) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.151 | 0.237 |
| R2 Adj. | 0.140 | 0.218 |
| AIC | 222.2 | 215.6 |
| BIC | 229.3 | 225.1 |
| Log.Lik. | -108.096 | -103.798 |
| RMSE | 0.93 | 0.89 |
## [1] 0.02668074
## Analysis of Variance Table
##
## Model 1: perc ~ vv
## Model 2: perc ~ vv + oc
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 78 54.640
## 2 77 52.586 1 2.0533 3.0066 0.08693 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | 1.182 | 1.098 |
| (0.114) | (0.122) | |
| vv | 0.353 | 0.327 |
| (0.062) | (0.063) | |
| oc | -0.145 | |
| (0.084) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.290 | 0.317 |
| R2 Adj. | 0.281 | 0.299 |
| AIC | 202.5 | 201.5 |
| BIC | 209.7 | 211.0 |
| Log.Lik. | -98.264 | -96.732 |
| RMSE | 0.83 | 0.81 |